This is great - very very helpful that you posted this death record! Below is an attempt at reading the handwriting.
First though, I'm not sure what you mean by "Aumonson, is believed to be Aumonson, Sweden, and not a last name." The death record is very clear that Carrie was born in Norway and Carrie's father is Peter Aumonson. Peter is his first name, Aumonson is his patronymic name. In the USA the patronymic name would be called a last name or surname. In Norway another name might come after Aumonson. It's not a permanent part of the person's name though. That third name is a place name, often called an address name. It tells where the person lives. When the person moves, the name changes. So yes, in Norway, Peter Aumonson's records might include yet another name after Aumonson. Is that what you meant when you said Aumonson is not a last name? Aumonson IS his last name in the sense that we Americans use the term "last name." You probably know all that and yet it might help some one else sometime.
(as an aside, I am privately suspecting the name might be Amundsen)
Okay, below is a try at reading the handwriting. Would be really great if others would also try reading this. As you say, it's hard to feel sure what the handwriting says.
Carrie Sofia Nordin [YAY! A MIDDLE NAME FOR CARRIE!]
Place of death: McCray Hospital, Valley City, Barnes, North Dakota
in hospital 13 days
in this community since 1955
Usual residence: La Moure county, N.D.
If foreign born, how long in USA? 1898
Color or race: W
Single, married, widowed, divorced: no answer/blank
Name of husband: Peter
Age of husband, if alive: no answer/blank
Birthdate of deceased: June 6, 1866
Age: 93 years, 2 months, 20 days
Usual occupation: housewife
Father's name: Peter Aumonson
Mother's maiden name: Janette Severson (?)
Informant's signature: no signature/blank
Burial, cremation, or removal: Burial
Place: High Prairie
Date of death: 8-26-1959
Doctor: J. P. Merritt, address: VC [Valley City]
Children: no answer/blank
Brothers and sisters: Mrs. Albert Aasland, 725 5th St St S.W.
Other relatives: Niece 1, nephew
Funeral held from: High Prairie
Day: Sunday, 2:30 pm (3:30 pm?)
Clergyman: Ernest Raam?
Pall bearers: Anton Nelson, Fred Johnson, XX? (can't read it), Garfield Anderson (LaXX?), Morris Olson, Ringvald Saarness (??)
Handwriting in the margin:
5553 [presumably a phone number]
--n Tcharge? [interment charge???]
1/2 m e
married July 29, 1903 [July 21? July 27?]
died Sept 1934 [presumably Peter Nordin's death date]
So this is why you chose the particular Anna Aasland - it's because she's in the same town where Carrie lived the last few years of her life. It could even be that the sister cared for Carrie in her last years. Did Carrie's niece and nephew (presumably the Wallins) share any stories or information about Carrie?
Can you get a hold of that marriage record from July 1903? I haven't searched this today but as I recall we didn't find it the other day online.
The more information you can gather in the USA, the better. Her immigration record, marriage record for her sister, obit for her sister, death record for her sister, etc. (I realize this is precisely what you are trying to do in this thread.) At the moment it's very tough to know where to begin looking in Norway, but with more records from the USA a clue as to the place might turn up. I'll return to helping with your search soon. Some of these records might not be online and might have to be requested (from the county, from the church, from a local volunteer in Valley City genealogy society, etc.)
Again thanks for posting this. All best